Compared to the 15th Scotts the 2nd infantry has more phase A infantry firepower and artillery. However, this comes at the cost of availability in both infantry quantity and infantry support. You will need to play an aggressive early game by taking ground and assaulting the enemy with your well-trained, specialized infantry and mortar teams. It is absolutely necessary that you utilize your phase A 2-star mortars in order to provide quick smoke screens to keep assaulting infantry safe from anything that could pin them down and slow their advance. While 2nd infantry is severely lacking in early game AT they have so much artillery that you can, and absolutely should, use it to shut down those units which are otherwise invulnerable to you. In practice this generally means perpetual smoke and shells to blind and disorient enemy heavy armor. Disoriented, miss-micro'd German armor makes a juicy target for your marauder recon units. Unlike the Scotts, you should be scoring kills every game with your marauder recon units. Additionally, be aware that the 2nd only has access to a 500m range MMG in phase A and is outranged by german HMG's. Those guns need to be shut down with artillery. The rest of the game is played more conventionally with increasingly spammable infantry, tanks and AT guns. What the 2nd lacks in armor it makes up for in artillery so, whether you like it or not, you're going to have to dig in and spam that shit.
What I've mentioned so far is myopic but I still consider it to be a decent summary of some idealized 2nd infantry gameplay. Realistically, you'll need to have some tactical flexibility. In my opinion they are an odd in-between division that has lost its role since its release in beta. For some time it was the only division with early access to cheap, well-trained infantry and in that environment the 2nd could succeed with this awesome "victory or death", "rip them from the land" "drown them in lead" kind of rolling assault style gameplay. It's like the developers watched the 5th episode of Band of Brothers, saw the scene where Easy Company throws down smoke, charges through an open field and obliterates a slew of Germans with a hail of artillery and rifle fire and then decided that they needed that in their game. Now, relatively, their infantry isn't particularly great and they don't have very much of it. In the current meta I recommend a more balanced approach. I particularly like the 1200m range HE 5 AV vehicle in the support tab. It provides terrific firepower and safe distances and is capable of destroying HT's and infantry, routing light armor, and destroying 1000m range AT guns more reliably than your mortars. Really, depending on what division you find yourself against, just be ready to shift your early game tactics to either use infantry to support your vehicles or your vehicles to support your infantry.