Budget may be the consideration. If he's on a free- even if he's on a large wage- on a one or two year contract his total cost of ownership would probably be less than buying a younger player of similar quality. If for example, Rodgers has 6 positions he wants to improve- and can spend money in four- and get cheaper temporary options in a couple of others- then players like Cole- might not be what we want right now, but as a stop gap to be replaced in the future, might not be so bad.
I agree, don't really want Cole, but I'm not the one watching Liverpool's bottom line. (hence, won't lambast the club if sign him)
Based on the above, Rodriquez definitely is portrayed as the better option. I'm not worried about his number of long balls... it shows he is capable of them when necessary (and we do use them strategically- we're not the Tika Takka that journalists like to claim we are)... we're not long-ball merchants, but we definitely, as a team, know how and when to use them. It doesn't mean that a player like Rod would have to use them, or even be encouraged to use them in large numbers. You can tell a player... "hey, don't hit so many long balls" that's a tactic thing- not necessarily a player trait, so unfair of article to penalize him on that.
Disposessions too is a grey area. If he is disposed more because he is playing a more risky attacking style (as suggested in article) then unfair to compare him to someone playing a more conservative defensive style.
I haven't seen all the defenders mentioned here play- so I can't make a truly educated or informed decision- the numbers seem to point to Rodriquez though- despite his two defecit areas.