I see some posters questioning the progress under EtH. Whereas they might ultimately be "proven right" in hindsight - and EtH might fail to bring us to next level, there is really not enough evidence yet to seriously question him at this stage (and many of them unfortunately resort to really flawed arguments and cherry-picking). Especially regarding comparing EtH unfavorably with Ole.
Going by results - let us compare like for like. We are a bit under a year under EtH. At the same point in time with Ole we were pre-Bruno and literally midtable (which is somehow often forgotten) whilst playing horribly. And by midtable, I mean literally. We were around 10th at some points in time. Went out at semifinals in all the cups in that season also, so EtH will most likely do better here also.
Regarding the squad - just mentioning EtH signings and not mentioning outgoings is blatant cherry-picking, sorry. Ole had at various points of his tenure the likes of Pogba, Cavani, fit Martial, a not-as-declined Ronaldo, Matic at a similar age to Casemiro at the start, Lukaku, Greenwood, a younger DDG closer to his peak etc etc. And especially if we start mentioning Sabitzer, Wout and Pellistri - we might mention the likes of Lingard, Mata and Pereira then. Yes, some of those players were old, some unfit/sulking etc etc - but EtH literally had both his two key midfield signings injured or suspended/being eased in for the large part of the season, basically no fit strikers etc. Point is, there is no evidence that EtH has a stronger squad, both on paper and in terms of what is available.
The squad stength argument is also good old "shifting the goalposts". Ole was lavishly praised for the 2019 transfer window when we were midtable "at least his signings were good" (check the Caf at the time of you do not believe me) - how does this window look now? (after a few years this actually turned into "oh, those were not his signings"). Notice that I won't credit EtH with transfers here - still early days (and I will actually somewhat criticize some aspects of the transfer policy under him later). We also had serious threads named "let Ole buy a whole new team over 2-3 years and only then judge him". And also the good old hindsight argument - until a year ago Ole was widely credited with "building a good squad for the new manager", where is this argument now? And I must say (also with hindsight and given the struggles of other managers with a lot better CVs) Ole did not do too badly given his profile (whilst being a bad appointment long-term and lost time still). But we have to apply similar standards to our managers, irrespective of whether they are club legends or not.
I agree that some of the aspects of EtH tenure are concerning - inconsistency in performances, stubbornness with tactics/selection (but for me it is mostly his seemingly free reign over transfers which should not continue - e.g. insisting on paying that much for Antony and then having to rely on the likes of Wout because of FFP- this is definitely on him), but so far most of them are "teething problems" to be expected in the first season after having taken over a really underperforming team and dealing with significant injuries & suspensions of key players. Again, he might ultimately fail but comparing him to Ole unfavorably at this stage does not stand to scrutiny, it really does not.
Finally, remember how Klopp and Pep's first seasons were constantly mentioned to put Ole's performance into perspective? Somehow this is also conveniently forgotten by EtH-critical posters now.