Kind of, but not really? It's a more complicated subject than you think.
Mozart was a child prodigy who wrote in dozens of different genres (string quartets, concertos, operas, symphonies, piano sonatas, etc.) in an era that was heavily focused on clarity, structure, and simplicity. He exemplified all these ideas, and is generally considered to have been a master of clarity and structure. He also added greater degrees of expression in drama in these forms in his later years. Musically, he represented the philosophies of the Enlightenment period and was their zenith.
Beethoven was also an absolutely monolithic figure in the history of music. He expanded the role of the musician/composer to being an artist, also wrote in dozens of genres, and expanded the forms and conventions of his predecessors to an extent never seen before. Almost every composer that followed Beethoven lives in his shadow (to a lesser extent, they did with Mozart as well) and their was a huge ideological debate on exactly HOW music should continue following Beethoven. I think, in the entire history of popular music, the only figures who come close to Beethoven's influence would be The Beatles.
Dream Theater is an important band, sure, but their scope and influence is very limited in the grand scheme of things. Dream Theater are mainly notable for taking the conventions established by the Progressive Rock artists of the 70s and early 80s and applying those to a metal idiom. Notably, they took the meter changes that 70s prog brought into the fray and pushed those further (in accordance with metal's more rhythmic focus) while mostly using them in the same way that the 70s prog bands did. Dream Theater's usage of rhythm and meter is great, for sure. How they use meters to emphasize the form and structure of their music is also great. Their use of harmony isn't really that notable or groundbreaking. Their use of counterpoint is okay, but not particularly great. They're also not really great orchestrators (sad to say). But again, their scope is very limited in to a few genres (Progressive Metal, Progressive Rock, Djent, and Symphonic Metal, for the most part), rather than nearly every practiced genre in a field. In terms of sheer influence, comparing Dream Theater to Mozart and Beethoven would be ridiculous.
That said, comparing metal bands (even prog metal bands) to classical composers in general is a bit silly. Their goals and techniques are COMPLETELY different. It'd be like comparing Skrillex and Johnny Cash. Sure, you could, but why would you? Johnny Cash is trying to tell a lyrical story. Skrillex is trying to get people to dance and trying to push the boundaries of sound design. They're apples and oranges. Classical music is mainly focused on form, harmony, counterpoint, and orchestration. Rhythm and meter are not nearly as important as in metal. You might be able to make some sort of comparison based on forms, but honestly they're different.
Even comparing a lot of classical composers/pieces is a little silly. I don't think any musicologist in their right mind would try comparing Chopin's Mazurkas to Wagner's Ring Cycles. They're totally different. Even comparing Beethoven's string quartets and piano sonatas in general seems a bit weird to me, unless you're focusing on one thing that Beethoven did in general and using them as example. You should look at each artist and piece/song on their own merit, in the context of the genre(s) it's in.
So, basically, I think you can compare them in a very few, select, limited amount of areas. But they emphasized different things and had different goals, so most comparisons would be fruitless.
Those composers such as Bach, Mozart, Chopin, Beethoven etc,, would all be impressed if they were around to hear DT's music. So yes, they are all in the same league imo.. 
Hmmm...I'm not quite sure about that tbh. Mozart, as I mentioned earlier, was from a period that emphasized clarity, structure, and simplicity. I don't know if he'd like it. Chopin was also more on the conservative side than a lot of people think, and was mainly focused on piano music. He probably wouldn't like it either. Bach is hard to say, but he was mainly a church musician and his biggest things were counterpoint and harmony (which DT isn't really very known for). I'd say a no for him too. Beethoven is kind of a toss up. He would have likely appreciated some elements of it and disliked others. He probably would have appreciated how loud it was in his older years tho haha.
I think, as far as composers go, the ones who would have likely liked DT would have been Liszt, Stravinsky, Gershwin, and Ravel I'd say. The last two I'm the least sure on. Rachmaninoff might have liked it too. The more conservative romantics like Saint-Saens, Brahms, Schumann, Bizet, and Mendelssohn probably would not. Haydn probably wouldn't. The Second Viennese school probably wouldn't like it. Debussy wouldn't have liked it much either (although he would have appreciated the rhythmic aspect of it). Wagner and Paganini are a toss up.
Topic: can you compare dream theater's music to big composers's music(mozart,bach) (Read 1926 times)