The greatness of Handel can be found if you don't stop at the style of the time. Other composers understood this greatness.
Some quotes (FWIW) to start
Mozart said that "Handel understands effect better than any of us -- when he chooses, he strikes like a thunderbolt... though he often saunters, in the manner of his time, this is always something there".
Haydn: C'est William Shield qui écrit: J'en profitai pour lui demander ce qu'il pensait du choeur "The Nations tremble at the dreadfoul sound" de Josuah. Il me répondit qu'il s'y connaissait depuis longtemps en musique, mais qu'avant d'entendre ce choeur, il n'avait réalisé qu'à moitié la puissance qui pouvait être la sienne et que certainement seul un auteur inspiré avait pu ou pourrait concevoir une oeuvre aussi sublime. (from a Haydn biography)
Translation: It's William Shield who wrote: I asked to Haydn what he was thinking of the "The Nations tremble at the dreadfoul sound" chorus from Josuah. Haydn said that before listening this chorus, he only realized the half of its the power and that only an inspired author could conceive a sublime work like this one.
Beethoven: "Go to him to learn how to achieve great effects, by such simple means" (e.g. Beethoven was amazed by the simplicity/efficacy of Handel's funeral march from Saul).
These quotes sum the main reasons why I like Handel's music.
1- Let's begin why the effects. He had great dramatic gifts. He knew how to use them. For the only purpose of the drama, he often went further than the operatic rules would permit. This dramatic sense can even be seen in his instrumental music.
But more than that, he was a keen psychologist. More than anyone composer during baroque era he develop characters in his operas/oratorios/cantatas who showed nature of human being with his qualities and flaws. His singers were not only high vocal performer (as the public wanted at this time), but characters having real feelings. On this aspect, he was the Mozart of baroque era.
2- Let's talk about his music's power. Many say that they find Handel too pompous. Even if Handel had to compose official music who could sound pompous, many people lack to understand that what they call pomp can be might. (And it starts to the fact that Handel is still unknown. Many people do not go further than Water Music and Fireworks Music. It easy to judge a compose when you only listen those 2 works)