Under both budgets on which the House will vote today domestic spending would be deeply cut over the next three years, but the Republican alternative would cut much more--about $100 billion as opposed to about $50 billion in the Democratic plan.

In particular, the Republican proposal would dig much deeper into programs for the poor. The food stamp and other nutrition programs would be especially hard hit. With the new cuts proposed by the GOP plus the cuts Congress voted last summer, spending next year on these programs would be a third below the level projected before Ronald Reagan took office.

In welfare programs that provide benefits in cash rather than in kind, Aid to Families with Dependent Children and Supplemental Security Income, the two years' cuts would reduce spending about a fifth. In the Medicaid program that helps pay poor people's medical bills, spending would be down about a sixth.

Here is how the cuts compare under the two proposals before the House, as well as the one already passed by the Republican Senate, which would cut domestic spending a little over $90 billion over the next three years:

The House Republican plan, sponsored by Reps. Robert H. Michel (R-Ill.) and Delbert L. Latta (R-Ohio), would cut about $103 billion over the next three years (fiscal 1983 to 1985) from what would be spent for domestic programs under current law after allowing for inflation. The House Democratic bill, sponsored by Rep. James R. Jones (D-Okla.), would cut about $49 billion from domestic programs in the same period; the budget resolution already passed by the Senate would cut about $93 billion.

Here are some of the key differences between the proposals:

Medicare--In the House debate on the budget two weeks ago, when no alternative won a majority, Democrats hit the GOP hard for proposing some $23 billion in cuts in the program which pays medical bills of the aged and disabled and is more for the middle class than the poor. The new GOP resolution would cut Medicare only $11.5 billion over the next three years, and sponsors claim none of the cuts would require higher payments by patients, although Democrats dispute this. The budget resolutions do not spell out how proposed savings should be achieved. That is left to other committees later. The House Democratic bill has a much smaller Medicare cut, $6.8 billion over three years; the Senate-passed budget bill calls for much larger cuts, about $18 billion over three years, with higher patient payments possible.

Medicaid--The House GOP proposal projects about $6.6 billion in cuts over three years; the House Democratic bill about $900 million; the Senate bill more than $2 billion.

Feeding programs--The House Republican bill would cut food stamps and child nutrition some $7.7 billion over the next three years, through curtailing cost-of-living increases and the amount of income that can be disregarded in calculating benefits, that is, the higher a recipient's income the lower his stamp allowance.

The House Democratic bill would make no major food stamp program cuts except for penalizing states that fail to reduce error rates. The Senate bill assumed about $3 billion in food stamp reductions over three years.

Cash programs--The House GOP bill would cut welfare outlays over three years about $3.4 billion by a variety of methods, including probably stepped-up work requirements and fewer income set-asides in figuring benefits. The House Democratic bill would go the other way, repealing some new eligibility requirements imposed on the working poor last year and making cuts only through penalties on the states for high error rates. The Senate-passed bill would cut about $1.5 billion over the next three years.

Housing--The House GOP bill would eliminate all new contracts for subsidized housing for the poor in fiscal 1983 and cancel some housing previously authorized. The House Democratic and Senate bills, by contrast, would allow over 100,000 new contracts in fiscal 1983 and subsequent years. All three bills make allowance for the new mortgage-interest subsidy program, designed to stimulate housing construction, that has passed both chambers in different forms and is threatened with a presidential veto.

Unemployment--Both House bills would allow funds for a 13-week extension of unemployment benefits for workers in high-unemployment states who have exhausted an initial 39 weeks available under two existing programs. The Democratic alternative would also repeal some restrictions on unemployment compenstion voted last year. The Senate budget contains neither provision.

Federal pay and retirement benefits--The House Republican bill would not impose any ceiling on cost-of-living increases for retired federal employes, but would limit federal pay increases to 4 percent annually over the next three years. The House Democratic bill also would impose no ceiling on retired worker increases, but would limit federal pay increases to 5 percent a year. The Senate-passed bill would forbid any increases in fiscal 1983 and limit increases thereafter to 4 percent for both. The House GOP proposal also contemplates a 2 percent reduction in the federal work force by 1985.