Is it advantageous to claim my son as a dependent since I am paying for his tuition?

Q. Is it advantageous to claim my son as a dependent since I am paying for his tuition?

A. No*. The parent who claims him as a dependent gets to claim the tuition credit (worth up to $2500), even if it was the other parent that actually paid the tuition.

Q. Can I reclaim my son as my dependent since we are divorced with my ex wife and she claimed him last year?

A. No.  That answer assumes your son lives with his mother most of the year.  If he lives with his mother, you can only claim him as a dependent, if she lets you (by signing and giving you form 8332).  And maybe not even then.  If he has reached emancipation age, the custodial parent is no longer allowed to release the dependency to the noncustodial parent.  The regular dependent rules govern. 

There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test.

A child of a taxpayer can still be a “Qualifying Child” (QC) dependent, regardless of his/her income, if:

1. He is under age 19, or under 24 if a full time student for at least 5 months of the year, or is totally & permanently disabled
2. He did not provide more than 1/2 his own support. Scholarships are excluded from the support calculation
3. He lived with the parent (including temporary absences such as away at school) for more than half the year

If he qualifies as his mother's QC, then you are barred from claiming him even under the Qualifying Relative rules. 

See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Return/INF12139.html

* There could be a situation where it would be better for you to claim him.  If the mother's income is low enough that she did not get the full $2500 credit (only $1000 is refundable).  But even then, you have to follow the dependent rules, so you might not even be allowed to claim him (and the credit)