Its an interesting debate.
Breaking it down...i see it this way...
Midfield
We've both lost important midfielders. United have lost Herrera and plan B Fellaini. Arsenal lost their best player last year..Ramsey
Pepe in a different position could replace Ramsey as a creator and scorer. Ceballos then adds another body for midfield albeit probably not having a major influence.
We've not directly replaced Herrera or Fellaini, but we did have some midfield bloat. McTom is fairly imposing and has arguably as much to his game as Fellaini, but more versatile. Maybe not quite as imposing in the box, but there is potential. He is a good blend of what those two could do albeit without the peak yet. Thus we are relying on potential.
Pereira is capable of moments of brilliance, again something Fellaini could do, but he doesn't have the energy, power and speed of Herrera. So in a way these two step up as maybe weaker players in terms of peaks, but more rounded in terms of offerings. Fred has all the energy of Herrera, but has not found his quality yet, but again provides another option as he did last year and might step up.
The real excitement in midfield in the AM role comes in a few different forms....Mata in the right position can be like a new signing. He has all the quality to boss that position in tight games requiring less speed. Lingard provides the energy against fast counter attacking teams.
But most exciting is Gomes who looks like he could have it all. Gomes could be the answer we were looking for, we just have to be brave enough to bed him in. Crystal Palace at home and Southampton away are prime games for this.
Arsenal probably currently have the better midfield in terms of consistency, but i think ours have potential for more momentary brilliance and that can win you games.
Defence
Arsenal lost Koscielny as captain, albeit a relatively weak one and have replaced with Luiz...no real change, albeit maybe more mistakes in Luiz, but i think overall he might be a better player.
In CB we've added a first teamer in Maguire so that's a clesr forward step. We also have Tuanzebe so again are more than covered with good quality.
Tierney adds cover and Bellerin returns at some point so they won't be as exposed on wing backs. Similarly, we have signed Wan Bisakka so are far less exposed than having Young there.
Our defence is unquestionably better than Arsenal's.
Attack
I've mentioned Pepe for Arsenal, who in a different position needs to replace what Ramsey gave. Ramsey's injury is what cost Arsenal that 4th spot. This does come with some risk, but no where near as much as the risks we are taking.
Losing Lukaku is a gamble. It's the 2+2=6 route, vs the 2+2+1=5, i.e. we have to hope the increased speed of play and increased opportunities makes up for Lukaku's ability to finish half chances. Lukaku also had a higher work rate than Martial, thus Martial needs to be far more present. In terms of chance finishing i don't dount Martial can step up and Greenwood also provides a new option.
The main question is simply the work rate to hunt out those chances. The goal Martial scored against Chelsea is a similar type of goal Lukaku would get, i.e. bossing it in the box to make sure the goal is forced in. If anything Martial was actually even more alive than Lukaku would be that close to goal. It's a promising show.
Overall
Before the Chelsea game and maybe as self presevation among friends who support other clubs, i said we'd come 5th behind Arsenal. It was incredibly hard to call as i don't think there is much between us. Similarly i think even Wolves and Everton will close the gap, but i don't believe it will be enough.
What it comes down to is a few uncertainties....
Will Pepe replace the influence Ramsey had. Immediately maybe he won't, longer term he might even be more influential. That is probably Arsenal's biggest question.
They will continue to leak goals, but Lacazette and Aubameyang will continue banging them in. Pepe is the tipping point of will they score one more than you!
For us anything we lose in Lukaku we gain in defence so I'm not too worried there and from a synergy perspective and with Greenwood i think we have a couple of aces up our sleeve that might mean we are better overall.
Midfield is the big question. Simply put, do we have enough quality. Take Pogba out and we need to be extra smart tactically. I still think Mata/ Lingard/ Gomes in that AM position could do enough to keep the cogs turning, but even then you still have to rely on Fred/ McTom and Periera or static matic to try and get a hold of the ball.
The positive about a weaker midfield is it might actually play to our advantage. Our defence are all killers, more often than not they'll get hold of the ball and they all have the ability to transition the play rapidly. Rashford/ Martial/ Greenwood/ James/ Chong will all thrive on quick counter attacks.
The Chelsea game was a great example of this. Chelsea didn't take their chances and we put the game to bed. If we had conceeded first we might have struggled to get past their midfield, but instead we took took first blood and didn't look back.
Wolves will be a big test. They like to counter, as do we. They won't expose themselves as much as Chelsea, but we can't afford to use Mata because we'll transistion too slowly on the counter.
It's the one type of game i think we might be inadequately tooled. Someone like Fernandes has the ability and energy to get back on the counter, but also to provide incision in attack. Do we really have anyone that can do that.
Lingard can provide the energy, but rarely incision. Mata can provide the incision, but no energy. Gomes could be a solution, but Wolves are physical and he might het get brushed aside. Pereira is maybe the most rounded, but won't get back fast enough and is only a little more incisive than Lingard.
I'd probably go with Fred and McTom as DM's, Pogba just ahead. Id then have Rashford, Martial and Greenwood forwards. This should provide enough quality in and around the box to craft chances.
How we handle this test will probably go some way to showing what we can do this season and thus how we compare to Arsenal.
The potential is there, but our biggest weakness in defence is our strongest weapon in attack. Who will punch first....it's not something Arsenal would consider because they have to keep attacking and have the quality to score.