izigame.me

Radiant Silvergun was originally developed by Treasure in the late 90's, and it's widely viewed as one of the greatest shmups of all time. It's also a spiritual predecessor to Ikaruga. Most notably, both games have extremely prominent scoring systems built around killing chains of like-colored enemies, though the specific rules are different. Both games also have excellent music and presentation, though Ikaruga understandably looks nicer being a more recent game.
While Ikaruga is the more famous game, in a lot of ways I actually prefer Radiant Silvergun. Typical of modern shmups, both games are extremely easy to "beat" by credit feeding, but the true test is whether you can beat the game in one credit. On first impression, both games are incredibly hard, but with a ton of practice, I did finally manage to 1CC Radiant Silvergun and get 100% achievements - two things I doubt I could ever do in Ikaruga.
There are a couple reasons for this. First, this port of Radiant Silvergun has a really great training mode that lets you practice small segments of the game. More importantly, it lets you lower the speed. Thus, you actually have time to analyze each section, devise your strategies, and then learn to execute your routes correctly before trying to execute them quickly. In a game so heavily based on chaining, it's impossible to overemphasize how helpful this is, and unfortunately Ikaruga doesn't have it.
Second, your ship in Radiant Silvergun is slower than in Ikaruga, but it has really precise tap movements. The game is also in a "wide vertical" format, giving you a lot more breathing room to maneuver. The game is really well calibrated to what your ship can and can't do, and I had a real sense of trust in the controls. My biggest criticism of Ikaruga is, too often it has these segments that just don't feel suited to your ship's tap movements or the screen's narrow aspect ratio.
Additionally, I really love your huge arsenal of weapons in Radiant Silvergun, and the huge number of spectacular boss fights. You have 6 missile weapons available at all times, plus a cool sword attack. This offers a ton of versatility and potential for player expression. Unlike Ikaruga, your ship can't change color and absorb like-colored bullets, but the sword does allow you to absorb certain bullets. Once you've absorbed enough, you can do a devastating super slash that also briefly renders your ship invincible, similar to bombing in a Cave game.
For these reasons, I'd say if you're just looking to mess around, both games are about equally good. But if you're looking to get serious and go for a 1CC, Radiant Silvergun is hands down the game to try first.