What are the major differences between spoken Standard Mexican Spanish and Standard European Spanish? What are the major written/grammatical differences? Is there any reason to think that the differences would make one variety more challenging to learn than the other?
There are no major differences, although it really depends on what you consider major. Although the comparison is fair, I do think there is a slightly bigger difference than that between American English and British English.
Please do note that someone from Mexico and someone from Spain can perfectly understand each other, although it is common in a long conversation for some words/expressions to require additional clarification or need to be understood from context (see point 3 bellow).
Accent is different. This is just personal choice, you should just choose whichever you like the most or is available.
Grammar is the same. Generally speaking grammar rules are identical (see point 3), this is mainly due to the fact that the Royal Spanish Academy (Real Academia Española) is the institution that regulates and ensures the stability of the Spanish language, including dialects. It is a Spanish (from Spain) institution, but, from Wikipedia, "it is based in Madrid, Spain, but is affiliated with national language academies in 22 other hispanophone nations" (*).
Words and expressions: Here is where we find the biggest difference. There are quite a good amount of words and expressions that we can classify into three groups:
- Expressions/words in one language that can are not used in the other one but can be understood by context.
- Expressions/words in one language that are neither used nor understood in the other one.
- Expressions/words that are misunderstood because they exist in both languages but have totally different meanings. Perhaps one of the most well known examples is the word coger.
"Te cojo luego en el bar" means "I pick you up later at the bar" in Spain. "Te cojo luego en el bar" means "I fuck you later in the bar" in Mexico and other latin american countries.
This answers your first question.
To the second one,
Is there any reason to think that the differences would make one variety more challenging to learn than the other?
There are no reasons to believe that one variety is more challenging. Choose based on other reasons like personal preference, abundance of friends that are native to one or the other variant or whatever fits you more or you think sounds best.
(*) Note how their dictionary captures all regional varieties of words, as in the example I gave with coger, whose meaning you can find here: https://dle.rae.es/?id=9fC4QbW (meaning 20 for Spain and 31 for Mexico in the example sentence).
In Mexican Spanish, the accent has a bit of an American tinge. The main difference that I find is the pronunciation of -z, in Spain they pronounce it with a bit of a lisp like -th. In Mexico however, they pronounce it as an -s or -z. Also there is once difference in the verb conjugations, in Spain they have -o, -as, -a, -amos, -ais, -an (-ar verbs), -o, -es, -e, -emos, -eis, -en (-er verbs) and -o, -es, -e, -imos, -is, -en. In Mexican Spanish, they they have no -ais, -eis, is.
Just like how we speak English slightly differently in the United States versus how they speak English in Australia, location impacts the Spanish language as well. With that being said, it's possible that if you visit Mexico but learned Castilian Spanish vs. Mexican Spanish, there may be certain words or things that don't translate the same as they would if you were to visit Spain and converse with native speakers there.