Significantly less so.
One way to measure the "regularity" of a language's verbs is, how much information do you need to memorize for each verb in order to conjugate it properly?
For Spanish, you don't need very much. If you have the infinitive, you can deduce the rest from that. There are a few irregular verbs, but those are a relatively small fraction of the total.
In Latin, you generally need to know four separate forms, the "principal parts", which provide information you can't get from the infinitive. For example, there are a few different ways to form the perfect (basically simple past) tense stem from the present stem: sometimes you add a -v- (amā- → amāv- "love"), sometimes you add an -s- (dīc- → dīx- "say"), sometimes you lengthen the vowel (ven- → vēn- "come"), sometimes you reduplicate the first syllable (curr- → cu-curr- "run"), and so on. There are a few general trends, like how most stems ending in -ā- add a -v-, but they're more like guidelines than hard rules. So you need to memorize the past stem alongside the present stem. And then you can usually figure out the supine stem from the past stem, but not always, so you need to memorize that too, and you can usually figure out the present stem from the infinitive stem, but not always, so you need to memorize that too, and in the end you're learning four separate forms for each verb.
I know that some verbs, e.g. ir, are weird because they come from multiple Latin words.
This is called suppletion, and happens in Latin as well as Spanish. (In fact, it happens in most inflecting languages—consider English "go" vs "went", or "be" vs "is" vs "was".) But suppletive verbs are generally a small minority, so they don't matter as much in terms of the overall regularity of the language.