I think this is a question of level of language. Plaisant sounds a bit more advanced than agréable to me. But the meaning is actually the same.

Plaisant can mean the same thing as the English pleasant: something that (some) people will like. It is very slightly dated in that sense. There is a connotation that something plaisant is likable or beautiful. More often, plaisant means something that might generate a smile or a chuckle, in particular (but not always) something that is not serious.

Agréable is a rather straightforward translation of pleasant.

I would have a hard time trying to describe the meaning of those words, but to me there is a slight difference:

• “plaisant” states the object as being likable to some extent, but without providing any reason. Also since it comes from the verb “plaire” I would even say it implies the object has an effect on the person : it makes her like it
• “agréable” is more focused on the nice feeling it conveys.

First and foremost, they both mean the same, that is, the English “pleasant”.

Then, as Shlublu mentions, “agréable” is more commonly¹ used in that sense, and “plaisant” can sound a bit more formal, therefore be less employed.

“Plaisant” is more often² used ironically to tell something ridiculous (relatedly to “plaisantin”, someone who makes light-hearted jokes). You can found examples in the Wiktionary (in french).

¹ I do hear “plaisant” more² in Canada, in its original “pleasant” sense.
² Still not a lot, but comparatively slightly more.

“Plaisant” has the sense of “pleasing” and is a bit subjective. Something that is “agreable” has a “positive” quality, a term that is a bit more objective.

If you are not a native french speaking, avoid using “plaisant”.
The word is quite old, formal and it would be difficult to use it properly without making your interlocutor smile.

Maybe in Québec, under the influence of english, it might not be the case.

I would securely use it as a synonym of “aesthetically pleasing”.

• “Un paysage plaisant. / Voici un tableau très plaisant”.

For foods and drinks, to express satisfaction.
– “Ce vin est fort plaisant”(note “fort” expresses some joviality).

To describe an amusing, embarassing, spicy situation, like a love scene, you can say :
– “une scène/situation plaisante”

Note that the contrary of “plaisant” , “déplaisant”, can be used with less precaution.

But I feel both words are on the formal side of french language anyway.
Prefer “agréable”, which is a real “passe-partout”.

Remember those words come from the verb “plaire”, a very important verb in french to express appreciation, that one should prefer to use instead of those somehow dusty/dull adjectives.

• “Ce tableau/ vin / paysage / livre / cette maison me plaît”. (regular)

• “Je me plais bien, ici”. (regular)

• “Ce n’est pas que votre compagnie me déplaise, mais je n’irai pas”. (formal)

• “Votre attitude me déplaît, monsieur”. (Hierarchical)

• “Ah, tu me plais bien, toi”. (To express affection)

• “Qu’est-ce qu’il me plaît, ce garçon”. (In love)

• “Ça, ça ne va pas lui plaire”. (regular /familiar)

And the idiomatic:

-“Dans la vie, on ne peut pas toujours plaire à tout le monde”.

That is how you’d rather express appreciation in french.