If you look at the things both bring to the table, you have to wonder who has the edge. The knee-jerk reaction is to say Weber-- if only for the physical force he brings to the table, as well as the cannon of a shot. The fact that the Predators are not a high-offensively minded team and Weber is good for 15 goals on the back-line while Suter has no more than eight in one season (2006-07).
Yet, the Predators have always been know and probably will always be known as a defensive team. That's where I think Suter has the edge. As good as Weber is in the offensive zone, Suter has the edge in his own zone and is probably the more of a shutdown man in comparison. If the Predators want to stick to that same scheme of defense first, Suter has to be the right choice to say around.
Of course, you look at what has happened in situations before. Most notably, the Ottawa Senators when trying to decide between Wade Redden and Zdeno Chara. In the end, the Sens made the wrong choice in picking Redden, as Chara was a monster back then and still is now. That's where the Predators are and this is a "damned if you do, damned if you don't" situation. If you let Weber go, you let a physical presence go with a helluva offensive upside. If you let Suter go, there goes a guy who could shutdown a team in a key situation.
Another side of the situation is Ryan Suter being the only one of the two being a UFA in the summer, while Shea Weber is a RFA. The danger in this is that Suter can be left with nothing coming back in return, which will ramp up his trade rumors. With Weber, the Predators could have other team dictate what the Predators have to pay if he is signed to an offer-sheet in the summer.
David Poile is a magician as a GM. If there's anyone who can balance out this situation, it could be Poile. While he's not a guy who will spend over his own means in order to appease the fan base who'd love to have all these guys signed to long-term deals. He won't hand-cuff his team in order to keep some guys who may not be able to pan out to their contractual terms. All eyes will be on Nashville until the trade deadline, then starting up again in June-- and mostly not for the hockey.