Both of these methods are suitable in any relational database, so you don't have to worry about that consideration. Both result in rather cumbersome queries. For the first method:
select . . .
from t left outer join
ref1
on t.ref1id = ref1.ref1id left outer join
ref2
on t.ref2id = ref2.ref2id . . .
For the second method:
select . . .
from t left outer join
ref1
on t.anyid = ref1.ref1id and anytype = 'ref1' left outer join
ref2
on t.anyid = ref2.ref2id and anytype = 'ref2' . . .
So, from the perspective of query simplicity, I don't see a major advantage for one versus the other. The second version has a small disadvantage -- when writing queries, you have to remember what the name is for the join. This might get lost over time. (Of course, you can use constraints or triggers to ensure that only a fixed set of values make it into the column.)
From the perspective of query performance, the first version has a major advantage. You can identify the column as a foreign key and the database can keep statistics on it. This can help the database choose the right join algorithm, for instance. The second method does not readily offer this possibility.
From the perspective of data size, the first version requires storing the id for each of the possible values. The second is more compact. From the perspective of maintainability, the first is hard to add a new object type; the second is easy.
If you have a set of things that are similar to each other, then you can consider storing them in a single table. Attributes that are not appropriate can be NULLed out. You can even create views for the different flavors of the thing. One table may or may not be an option.
In other words, there is no right answer to this question. As with many aspects of database design, it depends on how the data is going to be used. Absent other information, I would probably first try to coerce the data into a single table. If that is just not reasonable, I would go with the first option if the number of tables can be counted on one hand, and the second if there are more tables.