Is it true that traceroute directly reflects the speed or performance of the network? The reason I'm asking because I've tried tracerouting a site that has more hops, but it shows up faster in the browser (the sites are text based, comparable in size, and cache/history was cleared).

Anyone could explain?

Directly, absolutely not. It's quite often possible to get an indicator as to a possible problem from it, but certainly not by number of hops. Number of hops partially depends on configuration of the networks you travel on, being that most have invisible hops, but the number of them vary (routers your data travels through but doesn't show up in a traceroute), and others show a much higher percentage, but it doesn't say anything by itself.

And most importantly, the data might travel one path to the server and completely different path from the server to you.