Spoiler :On difficulties above Emperor, you'll always be behind in tech at the start, when you want to be attacking with Assyria, and as anyone you always want libraries.
It's also a misconception that you want to be behind with Assyria - in fact you want to be close to tech leader, since as with spies the technology you can steal is determined by your own tech level (you can't steal a tech you can't otherwise research), so if the defender has Civil Service but you don't yet have Mathematics, you're not going to be able to take Civil Service. Beyond that, you don't need to be behind in tech to gain a bonus, just not have techs the other civs do. This will usually be the case if you're going down the military path - you can steal techs like Philosophy or Compass that other civs will get before you even if they have fewer techs overall.
To the question at hand, I've had little success with Assyria on Emperor and Immortal and I'd agree that it might be a little weak:
The UA is certainly never going to compensate for teching, and often I find myself further behind trying Assyria than as a non-militaristic civ, so that I will often be in the situation where I can't capture cities quickly enough to compensate technologically. It may be best playing Assyria with the late game in mind, taking very beaker-intensive techs in late game war, but that loses all synergy with the siege tower.
The siege tower is powerful out of context, but it is not sufficient compensation for having no ranged siege units. You need several, or a couple of supporting melee units, to get the most from it, and you still can't skimp on ranged units. Unlike the Hun battering ram, the siege tower costs you the catapult, a long-lived unit at a critical game stage, and having no ranged siege before Physics is tough. Especially as the siege tower's effectiveness as a direct siege unit (rather than to support other units) tails off before the catapult's. The only effective use of siege towers I've seen has been from a Zulu AI that got them as a UU from a militaristic CS - and without supporting catapults they wouldn't have worked then.
The Royal Library has very little synergy with the civ's approach. It requires a Great Work of Writing, and you don't want to be devoting effort to teching to Drama and Poetry and then building a Writers' Guild early, plus the experience boost is less than you get from a barracks. So either you use it late, or you try to rely on looting a Great Work from a captured city. In either case, it's a somewhat pointless bonus since by that time you've built the units you need (particularly if you're successfully capturing cities).
Royal library is great for industry era military push after resting from the early war.
Basically a free BG (World wonder that gives +15xp) in every city. This allows triple promoted units from all cities!!! I would call it super op