The topic of the difference between addslashes() and mysql_escape_string() has come up a few times as of late, and I found myself actually having to look up the answer. I knew (as I hope you do) that the mysql_ version was better (mysql_real_escape_string() being better still), but I couldn't remember exactly why. In my research I found a bunch of miscellaneous blog posts that simply agreed with my understanding that mysql_escape_string() > addslashes(). Finally I found a post at NyPHP (of which I am a member) which described it in a bit more detail, listing some of the meta-characters that MySQL understands, but it didn't go into detail on exactly which characters were escaped. A chart, indicating my findings comparing addslashes to mysql_escape_string (all three sources of information are shown). I will consider the source and my test definitive (results after the jump).

		addslashes()	mysql_escape_string()
Ascii	Name	testing	testing	source
0	Null
8	Backspace
9	Tab
10	\n
13	\r
26	Substitute
34	"
39	'
92	\

So in conclusion: Use The Source! and you should use mysql_escape_string() over addslashes() to escape three additional characters, newline, carriage return, and substitute character.
Notes:
My test consisted of iterating through the ascii character chart, and comparing chr($i) to mysql_escape_string(chr($i)) then reporting if they didn't match (as would happen when something is escaped. Reading the source was looking at escape_string_for_mysql() in charset.c (part of mysql 5.0.45), and mysql_sub_escape_string() in libmysql.c shipped with the PHP 4 branch. The NyPHP document indicates that mysql_escape_string() and mysql_real_escape_string() all escape those same characters, it may be true that the real version escapes more, I intend to test more in the future.

Note^2
You shouldn't actually be using mysql_escape_string() you should be using mysql_real_escape_string() which takes the character set into account.